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Uncertain Principles

Physics, Politics, Pop Culture

Saturday, July 30, 2005

Missed Opportunity

I'm so out of touch. From this morning's local paper:

Michael Brigmond, Donald Lance and John Massey Jr. believe the end of the world is at hand. [...]

The three ministers are among the featured speakers at a four-day "End Time Prophecy Conference" at the Redemption Church of Christ of the Apostolic Faith in Troy, where Massey is the pastor.

Dammit, why doesn't anyone tell me these things. I mean, here we went and planned to have dinner with my parents tonight in Oneonta, and go see some Shakespeare up in Saratoga tomorrow. We're driving all over New York for entertainment, when we have crazy people right in our own back yard...

In my last post, I described an experiment to measure gravity at very short distances. It's really a tour de force experiment (as I've said numerous times on this blog), but at this point, you might reasonably ask "Who cares?"

The question of the short-distance behavior of gravity is closely tied to one of the great physics mysteries, namely "Why is gravity so weak?" That might not seem an obvious mystery-- gravity feels pretty substantial whenever I try to dunk a basketball, for example-- but gravity is, in fact, extremely weak. If you take two one-kilogram masses, each with an electric charge of one Coulomb, and put them close together, the electrostatic repulsion between them is 100,000,000,000,000,000,000 times greater than the attractive gravitational force between them. The force of gravity attracting you toward the Earth is pretty substantial, but only because the Earth is gigantic; the force of gravity between two people is completely negligible.

To the average person, this is one of those "Well, whatcha gonna do?" kind of issues-- if gravity is much weaker than the other forces, well, that's just the way it is. It's deeply troubling to theoretical physicists, though, because there's no reason why that should be the case. The world would probably be a pretty weird place if gravity were closer in magnitude to the other forces, but in a certain way of looking at the world, it would make a lot more sense.

Lots of people have struggled to find a halfway satisfying explanation for why gravity is so feeble, and one of the more popular explanations comes out of the world of string theory, as a side effect of the extra dimensions required for most string theories. As I understand it, it's not the reason why string theorists introduced extra dimensions in the first place, but having introduced extra dimensions in order to make some of the math work out, someone hit on the idea that extra dimensions can explain the weakness of gravity.

The central idea here is that the world we live in, which seems to have three spatial dimensions (north-south, east-west, and up-down) actually has a much larger number-- ten or eleven is the current consensus, I believe, but there have been suggestions involving something like twenty at various times. These would be spatial axes perpendicular to all three of the normal ones-- some direction you could potentially move in that is at right angles to all the others. It's a tough thing to visualize, with the standard explanatory tricks involving things like cartoon characters popping up out of the confines of their two-dimensional worlds.

The reason we don't usually notice these extra dimension (because you would think that somebody would've noticed a whole extra direction of motion sometime in the last few million years of evolution) is that they're just not very big. One way to think about it would be to view the universe as being kind of like a sheet of paper: from a distance, a sheet of paper is a pretty good approximation of a two-dimensional object. You've got to get pretty close before you can really see that there's a third dimension there at all. If you were inhabiting a sheet of paper, able to move through 8.5 or 11 inches in the plane, but ony a tiny fraction of an inch in or out of the page, odds are, you wouldn't really notice that third dimension at all.

What does this have to do with gravity? The idea is that gravity extends out into the other dimensions-- out of the surface of the paper, as it were. Gravity isn't actually weak, according to this view-- it's roughly the same strength as any of the other forces. It's just that it looks weak to us, because a lot of its strength is being used up in those tiny extra dimensions that we don't see.

(Some theories even have gravity extending out into nearby parallel universes (neighboring sheets of paper in the giant Xerox machine of the multiverse). You can find people who will argue that the gravitational effects of "dark matter" are really due to normal matter in some other universe affecting the motion of things in our universe. I'm not really sure what that means, either.)

If this is true, you would expect to see some effect of these extra dimensions when you start to look at interactions between objects on roughly the same scale as the size of those extra dimensions. In the same way that you have to get pretty close to a piece of paper before you notice its thickness, you need to look on a really small scale before you notice these extra dimensions. The tool you use to "look" at them, in this case, would be gravity. Specifically, if gravity is really strong in those other dimensions, then you should start to see that extra strength when you look at two objects separated by about the same distance as the extent of one of those dimensions.

The clearest explanation I've heard of why you expect to see something happen on a short length scale requires a diagram, so you'll have to forgive some more ASCII art (I try to keep this blog image-free, for politeness). In this case, you want to imagine a nearly one-dimensional universe, which is very long in one direction (across the page), and very short in a second dimension (bounded by "~" characters). If you look at the lines of force emanating from a little NetHack guy stuck in this world, what you see is something like this:

This is supposed to represent lines emanating from the "@" in all directions, and then bending away from the edges of the "universe" to travel more-or-less straight down the line (the "'" and "." are place-holders for nonexistent shallower dashes...). A distant observer (the "$" stands for "$tring theorist") will determine the strength of the force he or she sees from the density of lines passing through some region of space (between the "+" signs, say). In this toy model, that number remains more or less constant until you get pretty close-- there's only one line between the "+" signs for most of that length. Somewhere around the vertical line ("|"), there are suddenly three lines, and then five, and our intrepid little $ will start to notice that the lines are diverging from a point, and not just a uniform bundle after all. The distance at which that starts to become apparant is similar to the scale of the small "extra" dimension.

Opinions vary as to the size of those extra dimensions in a better-drawn world, but everyday sizes have more or less been ruled out because gravity looks nicely Newtonian on those scales. There are some theories that put the size of the extra dimensions at tens or hundreds of microns (0.01-0.1 mm), which is a scale that's just barely accessible to the Eot-Wash expriments. And right at the very smallest separations at which they can measure the force of gravity, they see a slight change. It's a very preliminary result, and they're working to confirm it, but the group doing the experiments has a very solid reputation as a cautious bunch of people, so many people tend to think that if they're willing to mention it in public, they must have some confidence that it's a real effect, and not just noise.

Unfortunately for the really simple models of extra dimensions, the sign of the effect is wrong. What they see is a slight weakening of the force of gravity, where the simplest string theory model says extra dimensions ought to make the apparent strength of gravity increase. If the result holds up, it'll be the first real experimental test of a prediction of string theory, and there will presumably have to be some scrambling to accomodate it. That's when things will get interesting.

(I should note that the talk I saw on the experiment back at DAMOP mentioned a different model (not string theory) that would lead to a weakening of gravity at short distances. I don't recall any of the details of the explanation, though. Lubos Motl refers to it as "fat gravitons", and the idea seems to be that for whatever reason, gravity has a characteristic length scale, and just doesn't work at really short distances. It's sort of hard to see why that should be the case, but then, it's hard to see why there should be a whole bunch of tiny little extra dimensions...)

The string theory post has generated some lively debate, so I'll try to follow it up a bit more with some attempts to describe a couple of experiments that aim to test some of the basic predictions of theories beyond the Standard Model of particle physics.

Of course, my motive in this is not merely a cynical attemt at traffic generation (because, really, there are easier ways to get noticed than struggling to explain the details of very complicated physics experiments to the laity). There's also a certain element of annoyance at string theorists-- specifically, the heavy hitters in the comments at Cosmic Variance, who won't answer a direct question about experimental results. It's been asked three times, and the closest thing to a detailed answer it's received is from a non-native speaker of English, and thus all but incomprehensible.

(If you're wondering why string theorists have a reputation for arrogance and disdain for experiment, well, this really doesn't help. It's almost certainly not the simple yes-or-no question that it appears, but it surely deserves a response, even if the answer is "It's really complicated.")

So, in the absence of an actual string theorist willing to talk about it, I'll attempt to explain what's being asked in this comment:

If, as rumored, experiments show that gravity weakens at small distances, would this be a serious blow to string theory?

The question is a reference (I think) to some recent preliminary results by the "Eot-Wash" group at the University of Washington. These guys are working on making very sensitive measurements of the force of gravity at short length scales.

The basic expression for the gravitational force between two objects was discovered by Isaac Newton, and it says that the force between two objects is given by the gravitational constant (6.7 x 10-11 N m2/kg2, a very small number) multiplied by the masses of the two objects, divided by the square of the distance between them. The forces involved are really tiny, unless one of the two masses is huge, but if you're clever, you can measure them, and the 1/R2 dependence has been verified over a wide range of distances, from centimeters to the size of the Solar System.

There are some people out there who think that the theory may need to be modified on extremely long length scales (distances comparable to the size of entire galaxies or clusters of galaxies). There are also some predictions that gravity might look different on very short lengths scales-- a tenth of a milimeter or below. That's what the EotWash group is testing.

Amazingly, the basic method they're using to measure the influence of gravity hasn't changed since the late 1700's. In 1783, a fellow named Henry Cavendish came up with the idea of a "torsion balance" to measure gravity. The classic Cavendish experiment uses a dumbell-shaped weight hung from a very fine wire. If you bring two test masses close to the ends of the dumbell, on opposite sides, the gravitational force between the test masses and the dumbell will cause the dumbell to twist, with the amount of twist depending on the magnitude of the force.

What they're doing in Washington is an ingenious update of the Cavendish experiment. Instead of a dumbell, they use a disc with a bunch of holes drilled in it-- the spots where the holes aren't are effectively like the masses at the ends of the dumbell, only there are more of them, and they're symmetrically distributed. The disc is still suspended by a very fine wire, but instead of test masses ont the outside, it's suspended over a set of two more discs with holes in them: a thin top disc, and a thicker disc beneath it, with the holes offset from one another.

If you'll forgive a little ASCII art, a side view of the test discs would look something like this:

The point of this odd arrangement is that the two discs should exactly cancel one another. The missing force due to the holes in the top disc is supplied by the solid bits of the bottom disc, which are more massive, but farther away. And the extra force due to the solid bits of the top disc are offset by the missing material in the holes in the bottom disc.

If you take either test disc by itself, and rotate it slowly beneath the pendulum, you should see a periodic twisting of the pendulum, as it's tugged back and forth as the holes rotate by. If you stack the two on top of each other, and then rotate them, you should see basically nothing, as the contributions cancel each other out. Provided, that is, that gravity continues to obey Newton's law (which is what's used to calculate the thickness of the discs, and the arrangement of the holes). If gravity gets stronger or weaker as you bring the test discs closer to the surface, you should see a clear signal.

They've done this basic experiment a bunch of times already, moving to smaller and smaller separations between the torsion pendulum and the test discs. Every time, they've had a null result-- gravity still agrees with Newton's three-hundred-year-old result.

Except, at DAMOP, someone from the Washington group presented highly preliminary results that might show an effect-- a slight weakening of the force of gravity at distances of less than a tenth of a millimeter. These are extremely preliminary numbers, and the possible signal comes right at the point where their everything is starting to crap out, but they're a cautious bunch, and for them to report it at all means that they think there's at least a chance it's a real signal, as opposed to just noise.

They're re-tooling now to do an even more sensitive test, at even smaller distances, so we'll see if this result holds up. If it does, that will be big news, though what this all has to do with string theory will wait for a later post...

I'm probably one of about eight people on earth with two weblogs who hasn't already posted detailed Harry Potter comments on either of them. This, of course, is a situation that cannot be allowed to continue. hence this post.

iTunes has finally finished downloading the songs I bought the other night, and the new batch has been thrown into the "Party Shuffle" mode. I went to the iTunes store to buy a couple of albums by KEXP acts, but got sucked in by the "iTunes Essentials" lists, and wound up buying a bunch of singles off the "One Hit Wonder" lists for the 80's and 90's, along with a bunch of other cheeseball stuff from various 80's subcategories.

Which means that, mixed in with new tracks by Youth Group, Crooked Fingers, the Shout Out Louds, and Devin Davis (the last was a CD purchase, because Lonely People of the World Unite! isn't on iTunes), there are occasional blocks like:

It's always faintly disturbing to me to discover the degree to which my musical tastes locked into place at about age fifteen. But, hey, synth-pop is coming back into style, so maybe I'm just avant-garde...

Posting this is probably at least as damaging to my tenure prospects (among the Ivan Tribbles of the world, anyway) as anything I could write about internal campus politics. But I can't help myself.

Regarding the little dialog box reminding me to back up my purchased music: it's a lovely thought, thanks for caring, but would it be too much to ask to have the downloading continue in the background while you prompt me?

You see, much as it may surprise you to hear this, when I purchase a hundred-odd songs from your store, I don't actually intend to sit in front of my computer for the entire download process. Particularly when the process is initiated at 11:00 at night.

It's somewhat irksome to go to bed, and wake up expecting to listen to new music (or, well, the large amount of 80's cheese that I bought last night), and find that only three songs managed to download before the whole thing came to a halt for your little reminder.

Just a thought.

And while I'm at it, what's the deal with songs being "No Longer Available" via iTunes? I understand physical CD's going out of print, because of the production and storage costs. But electronic files? What's the logic of that?

(That one, at least, has all the hallmarks of a record company decision: it's the sort of thing that might be motivated by a desire to squeeze more money out of music buyers, and it's also idiotic. Really, the people running most record companies are just too stupid to be trusted to manage a 7-11. The fact that they stay in business is a wonderful testament to the power of corruption.)

This is mostly a throwaway post to cover a template update (you're smart people, you can identify the new sidebar links on your own), but here are three links that might be interesting, in order of decreasing gravity.

Finally, if you woke up this morning saying "You know, what I need today is a weird little Japanese language Flash game in which you attempt to keep an angry little man from grabbing your mouse pointer," well, have I got a link for you. (Via a mailing list.)